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In mathematics, a multiplication table (sometimes, less formally, a times table) is a mathematical table used to define a multiplication operation for an algebraic system. The decimal multiplication table was traditionally taught as an essential part of elementary arithmetic around the world, as it lays the foundation for arithmetic operations ...
The inverse operation of multiplication is division. For example, since 4 multiplied by 3 equals 12, 12 divided by 3 equals 4. Indeed, multiplication by 3, followed by division by 3, yields the original number. The division of a number other than 0 by itself equals 1. Several mathematical concepts expand upon the fundamental idea of multiplication.
The combination of these two symbols is sometimes known as a long division symbol or division bracket. [8] It developed in the 18th century from an earlier single-line notation separating the dividend from the quotient by a left parenthesis. [9] [10] The process is begun by dividing the left-most digit of the dividend by the divisor.
Thought of partitively, a division problem might be solved by sorting the initial quantity into a specific number of groups by adding items to each group in turn. For instance, a deck of 52 playing cards could be divided among 4 players by dealing the cards to into 4 piles one at a time, eventually yielding piles of 13 cards each.
In approximate arithmetic, such as floating-point arithmetic, the distributive property of multiplication (and division) over addition may fail because of the limitations of arithmetic precision. For example, the identity 1 / 3 + 1 / 3 + 1 / 3 = ( 1 + 1 + 1 ) / 3 {\displaystyle 1/3+1/3+1/3=(1+1+1)/3} fails in decimal arithmetic , regardless of ...
For instance, in GF(5), 4 + 3 = 7 is reduced to 2 modulo 5. Division is multiplication by the inverse modulo p, which may be computed using the extended Euclidean algorithm. A particular case is GF(2), where addition is exclusive OR (XOR) and multiplication is AND. Since the only invertible element is 1, division is the identity function.